solve the equation: with Logarithm & one word problem

the stress i had a few days has went down so much since i became a member here, i actually feel prepared for my test coming up thanks to all of you. out of the 45 problems these are the last few im having serious problems with, i wish i understood these instead of bugging you guys haha

these last 4 problems i cant get a single answer.. problems #20 #21 and #22

problems #24 is a word problem that i cant figure out as well, help with any problems will be much appreciated.

i scanned the packet, here are the few problems im having trouble with.

the test is friday and i want to know the material as best as possible because the last test i failed. i normal dont fail things, its just harder for me to understand math more than others. its very frustrating

the stress i had a few days has went down so much since i became a member here, i actually feel prepared for my test coming up thanks to all of you. out of the 45 problems these are the last few im having serious problems with, i wish i understood these instead of bugging you guys haha

these last 4 problems i cant get a single answer.. problems #20 #21 and #22

problems #24 is a word problem that i cant figure out as well, help with any problems will be much appreciated.

i scanned the packet, here are the few problems im having trouble with.

the test is friday and i want to know the material as best as possible because the last test i failed. i normal dont fail things, its just harder for me to understand math more than others. its very frustrating

To #20:

Two logarithms are equal if their arguments are equal too:

Solve for x

to #21

Use the base-change-formula to get equal bases for all logarithms:

Since your equation becomes:

Therefore

Solve for x.

to #22:

Therefore:

Solve for x. Keep in mind that a logarithm is only defined for positive numbers.

Number 24 isn't really a word problem. They are asking you to solve the equation 1+ 1.5 ln(x+1)= 10. As always, you solve an equation by "backing out": subtract 1 from both sides to get 1.5 ln(x+1)= 9. Divide both sides by 1.5 to get ln(x+1)= 9/1.5= 6.

Notice that each step has been an "inverse"- the opposite of some operation. Initially, we had 1 added on the left so we do the opposite- subtract 1 from both sides. Then we had 1.5 multiplying the function of x so again we do the opposite- divide both sides by 1.5. Now we have a natural logarithm. What is the "opposite" of that? The exponential! ln(x) and are "inverse functions": and .

Taking the exponential of both sides, .

Finally, of course, subtract 1 from both sides. . If you want a decimal (but only approximate) answer, use a calculator.

Number 24 isn't really a word problem. They are asking you to solve the equation 1+ 1.5 ln(x+1)= 10. As always, you solve an equation by "backing out": subtract 1 from both sides to get 1.5 ln(x+1)= 9. Divide both sides by 1.5 to get ln(x+1)= 9/1.5= 6.

Notice that each step has been an "inverse"- the opposite of some operation. Initially, we had 1 added on the left so we do the opposite- subtract 1 from both sides. Then we had 1.5 multiplying the function of x so again we do the opposite- divide both sides by 1.5. Now we have a natural logarithm. What is the "opposite" of that? The exponential! ln(x) and are "inverse functions": and .

Taking the exponential of both sides, .

Finally, of course, subtract 1 from both sides. . If you want a decimal (but only approximate) answer, use a calculator.

ok thank you so much! that really helped me ALOT

for #23 i got 219 as the answer.. but i cant find what point is on the graph of G.. answers A and C both have 219.. but i cant figure out the second point. thanks again in advance, you are a really big help for me